Mathematical Sciences: Mathematical and Computational Problems in Object Recognition

该研究计划的重点是数学方面的 物体识别 有两类问题。第一 是在场景中定位的刚性物体的识别， 任意旋转、位置和比例。 大量的保留节目 假设形状是预先已知的，问题是， 设计计算效率高的算法， 这些对象中的哪些（如果有的话）存在于给定场景中。 将探讨顺序和适应性战略，其中 进行一系列基于图像的观察，选择 一个观察结果取决于以前的结果 意见。 与编码理论有着密切的联系， 序贯实验设计，多臂强盗问题， “二十个问题”的游戏，当然，以前的工作， 机器视觉 第二类问题是识别非刚性， 或可变形的物体。 例子包括手写数字 和各种生物形状，如树叶，手，细胞器， 在这里，形状建模的问题似乎是中心。 一个 提出了一种基于变形模板的方法。 模板 是捕捉全球特征的原型，而 变形是随机变换，满足一定的 规则性约束，这些约束作用于模板以生成 一个物体的可能性。 提出的形状模型 提出了某些识别算法，这些算法将 在各种应用领域进行了探索。

The research program focuses on mathematical aspects of object recognition. There are two classes of problems. The first is the recognition of rigid objects positioned in a scene at arbitrary rotations, locations, and scales. A large repertoire of shapes is assumed known in advance, and the problem is to then devise computationally efficient algorithms for recognizing which, if any, of these objects are present in a given scene. Sequential and adaptive strategies will be explored, in which a sequence of image-based observations is made, with the choice of an observation depending upon the results of previous observations. There are close connections to coding theory, sequential design of experiments, multi-armed bandit problems, the game of "twenty questions," and, of course, previous work in machine vision. The second class of problems is the recognition of nonrigid, or deformable, objects. Examples include handwritten numerals and various biological shapes, such as leaves, hands, organelles, etc. Here the issue of shape modeling appears to be central. An approach through deformable templates is proposed. Templates are prototypes which capture global characteristics, whereas deformations are random transformations, satisfying certain regularity constraints, that act upon templates to produce the possible presentations of an object. The proposed shape models suggest certain recognition algorithms, and these will be explored in a variety of application areas.